Trapping the radioactivity and waiting
How do you contain radioactivity long enough for it not to come into contact with the environment? That is the issue with the most highly radioactive waste. One solution is to incorporate it into a glass matrix that is highly resistant to radiation and water damage. A block of glass like the one in the photograph could trap radioactive atoms for thousands of years, by the end of which the original radioactivity would have almost completely disappeared through natural decay. The host rock would then contain the remaining radioactivity.